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r = \frac{3 + \sqrt141}3 - IX Labs

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Time span: 30 years. Increase: 26.8 − 25.4 = 1.4°C. Rate: 1.4 ÷ 30 = 0.0466... °C/year. From 2020 to 2050 is 30 more years. Increase: 30 × 0.0466... = 1.4°C. Temperature in 2050: 26.8 + 1.4 = 28.2°C.

📌 A geographer models urban sprawl using a circular expansion model. If the urban boundary grew from radius 5 km to 8 km over 10 years, by what percentage did the area increase?

📌 Initial area = π × 5² = 25π km². Final area = π × 8² = 64π km². Increase = 64π − 25π = 39π km². Percentage increase = (39π ÷ 25π) × 100% = (39 ÷ 25) × 100 = 156%.

📌 A climate model predicts that global average temperature will rise by 0.4°C per decade. If the temperature in 2020 was 14.8°C, what will it be in 2100?

📌 From 2020 to 2100 is 8 decades. Increase = 8 × 0.4 = 3.2°C. Temperature in 2100 = 14.8 + 3.2 = 18.0°C.

📌 #### 18.0A linguist analyzing historical texts uses a language model to compute semantic drift over time, measuring change in word usage frequency across 5 decades. The model assigns drift scores: 0.8, 1.2, 1.5, 0.9, and 1.6. What is the mean absolute deviation of these drift scores from the mean?

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